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On a PDE-based material parameter identification problem with contact constraints

  • Simon Hubmer
  • Stefan Kindermann
  • Ekaterina Sherina
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Abstract

We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or indenter. More generally, it serves as a benchmark for the analysis of more complex contact problems and the development of corresponding reconstruction algorithms. In this paper, we discuss both the forward and inverse parameter estimation problems, as well as uniqueness and non-uniqueness issues caused by the contact constraints. Furthermore, we consider the design and implementation of reconstruction approaches which we test on numerical examples, illustrating both uniqueness and non-uniqueness as well as parameter identifyability.

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Cite

BibTeXRIS
BibTeX
@misc{hubmer2026pdebased,
  title = {{On a PDE-based material parameter identification problem with contact constraints}},
  author = {Simon Hubmer and Stefan Kindermann and Ekaterina Sherina},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.08514},
  eprint = {2605.08514},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.08514},
}
RIS
TY  - UNPB
TI  - On a PDE-based material parameter identification problem with contact constraints
AU  - Simon Hubmer
AU  - Stefan Kindermann
AU  - Ekaterina Sherina
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2605.08514
UR  - https://arxiv.org/abs/2605.08514
AB  - We consider the identification of a scalar coefficient in a PDE-based parameter estimation problem with contact constraints. The considered problem can be used as an idealized model of a membrane under forces, constrained by a barrier or indenter. More generally, it serves as a benchmark for the analysis of more complex contact problems and the development of corresponding reconstruction algorithms. In this paper, we discuss both the forward and inverse parameter estimation problems, as well as uniqueness and non-uniqueness issues caused by the contact constraints. Furthermore, we consider the design and implementation of reconstruction approaches which we test on numerical examples, illustrating both uniqueness and non-uniqueness as well as parameter identifyability.
ER  -